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   "source": [
    "# Reference: https://jupyterbook.org/interactive/hiding.html\n",
    "# Use {hide, remove}-{input, output, cell} tags to hiding content\n",
    "\n",
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *\n",
    "\n",
    "import plotly.figure_factory as ff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-cell"
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   "outputs": [],
   "source": [
    "trees = pd.read_csv('data/black_spruce.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": [
     "remove-cell"
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   },
   "outputs": [],
   "source": [
    "trees['status_0_1'] = (trees['status'] == 'fallen').astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-cell"
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   },
   "outputs": [],
   "source": [
    "splits = [4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 25, 32]\n",
    "tree_bins = (\n",
    "    trees[\"status_0_1\"]\n",
    "    .groupby(pd.cut(trees[\"diameter\"], splits))\n",
    "    .agg([\"mean\", \"count\"])\n",
    "    .rename(columns={\"mean\": \"proportion\"})\n",
    "    .assign(diameter=lambda df: [i.right for i in df.index])\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "remove-cell"
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   "source": [
    "fig = px.scatter(\n",
    "    tree_bins, x=\"diameter\", y=\"proportion\", size=\"count\",\n",
    "    labels={\"diameter\": \"Tree diameter (cm)\", \"proportion\": \"Proportion down\"},\n",
    "    width=450, height=250,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling Proportions (and Probabilities)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that when we model, we need to choose three things: a model, a loss function, and a method to minimize the average loss on our train set. In the previous section, we chose a constant model, the 0-1 loss, and a proof to fit the model. However, the constant model doesn't incorporate predictor variables.\n",
    "In this section, we address this issue by introducing a new model called the *logistic* model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To motivate these models, notice that the relationship between tree diameter and the proportion of downed trees does not appear linear. For demonstration, let's fit a simple linear model to these data to show that it has several undesirable features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the techniques from {numref}`Chapter %s <ch:linear>`, we fit a linear model of tree status to diameter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "X = trees[['diameter']]\n",
    "y = trees['status_0_1']\n",
    "\n",
    "lin_reg = LinearRegression().fit(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we add this fitted line to our scatter plot of proportions: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-04-02T16:07:18.026129Z",
     "start_time": "2018-04-02T16:07:18.007888Z"
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    "tags": [
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            "showline": true,
            "ticks": "outside",
            "zeroline": false,
            "zerolinecolor": "rgb(36,36,36)"
           },
           "zaxis": {
            "backgroundcolor": "white",
            "gridcolor": "rgb(232,232,232)",
            "gridwidth": 2,
            "linecolor": "rgb(36,36,36)",
            "showbackground": true,
            "showgrid": false,
            "showline": true,
            "ticks": "outside",
            "zeroline": false,
            "zerolinecolor": "rgb(36,36,36)"
           }
          },
          "shapedefaults": {
           "fillcolor": "black",
           "line": {
            "width": 0
           },
           "opacity": 0.3
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "baxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           },
           "bgcolor": "white",
           "caxis": {
            "gridcolor": "rgb(232,232,232)",
            "linecolor": "rgb(36,36,36)",
            "showgrid": false,
            "showline": true,
            "ticks": "outside"
           }
          },
          "title": {
           "x": 0.5,
           "xanchor": "center"
          },
          "width": 350,
          "xaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          }
         }
        },
        "width": 450,
        "xaxis": {
         "anchor": "y",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          2.1225570831691045,
          33.926311262779556
         ],
         "title": {
          "text": "Tree diameter (cm)"
         },
         "type": "linear"
        },
        "yaxis": {
         "anchor": "x",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          -0.17412792022836332,
          1.6210911718883425
         ],
         "title": {
          "text": "Proportion down"
         },
         "type": "linear"
        }
       }
      },
      "image/png": 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   "source": [
    "X_plt = pd.DataFrame(\n",
    "    {\"diameter\": np.linspace(X[\"diameter\"].min(), X[\"diameter\"].max(), 10)}\n",
    ")\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=X_plt['diameter'], y=lin_reg.predict(X_plt), mode=\"lines\")\n",
    ")\n",
    "\n",
    "fig.update_layout(showlegend=False)\n",
    "fig.show()"
   ]
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    "Clearly, the model doesn't fit the proportions well at all. There are several problems:\n",
    "\n",
    "+ The model gives proportions greater than 1 for large trees.\n",
    "+ The model doesn't pick up the curvature in the proportions.\n",
    "+ An extreme point (such as a tree that's 30 cm across) shifts the fitted line to the right, away from the bulk of the data.  \n",
    "\n",
    "To address these issues, we introduce the *logistic model*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Logistic Model "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic model is one of the most widely used basic models for classification and a simple extension of the linear model. The *logistic function*, often called the *sigmoid function*, is defined as: "
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "$$\n",
    "\\textbf{logistic}(t) = \\frac{1}{1+\\exp(-t)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{warning}\n",
    "\n",
    "The *sigmoid* function is typically denoted by $\\sigma(t)$. Sadly, the Greek letter $\\sigma$ is widely used to mean a lot of things in data science and statistics, like the standard deviation, logistic function, and a permutation. You'll have to be careful when seeing $ \\sigma $ and use context to understand its meaning.\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the logistic function to reveal its s-shape (sigmoid-shape) and confirm that it outputs numbers between 0 and 1. The function monotonically increases with $ t $, and large values of $ t $ get close to 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-04-03T08:20:28.586913Z",
     "start_time": "2018-04-03T08:20:28.583811Z"
    }
   },
   "outputs": [],
   "source": [
    "def logistic(t):\n",
    "    return 1. / (1. + np.exp(-t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-04-03T08:20:28.597034Z",
     "start_time": "2018-04-03T08:20:28.588719Z"
    },
    "tags": [
     "remove-cell"
    ]
   },
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    "t = np.linspace(-5, 5, 50)\n",
    "sigmoid_line = go.Scatter(\n",
    "    name=\"Logistic Function\", x=t, y=logistic(t), mode=\"lines\"\n",
    ")\n",
    "\n",
    "fig = go.Figure([sigmoid_line])\n",
    "fig.update_layout(width=400, height=250)\n",
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    "Since the logistic function maps to the interval between 0 and 1, it is commonly used when modeling proportions and probabilities. Also, we can write the logistic as a function of a line, $\\theta_0 + \\theta_1 x$:"
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    "$$\n",
    "\\sigma\\left(\\theta_0 + \\theta_1 x\\right) = \\frac{1}{1+\\exp(-\\theta_0 - \\theta_1 x)}\n",
    "$$"
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  {
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   "source": [
    "To help build your intuition for the shape of this function, the following plot shows the logistic function as we vary $\\theta_0$ and $\\theta_1$:"
   ]
  },
  {
   "cell_type": "code",
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  {
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   ],
   "source": [
    "fig = make_subplots(rows=1, cols=3)\n",
    "\n",
    "from itertools import cycle\n",
    "styles = cycle(['dashdot', None, 'dot'])\n",
    "\n",
    "row = col = 1\n",
    "for theta1 in [1, 5, -1]:\n",
    "    for theta0 in [2, 0, -2]:\n",
    "        fig.add_trace(go.Scatter(name=f\"{theta0} + {theta1}x\", \n",
    "                                 x=t, y=logistic(theta0 + theta1*t),\n",
    "                                 mode=\"lines\", line=dict(dash=next(styles))),\n",
    "                      row=row, col=col)\n",
    "    col += 1\n",
    "        \n",
    "fig.update_layout(width=800, height=250)        \n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that changing the magnitude of $ {\\theta}_1 $ changes the sharpness of the curve; the farther away from 0, the steeper the curve. Flipping the sign of $ {\\theta}_1 $ reflects the curve about the vertical line $x=0$. Changing $ \\theta_0 $ shifts the curve left and right."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The logistic function can be seen as a transformation: it transforms a linear function into a nonlinear smooth curve, and the output always lies between 0 and 1. In fact, the output of a logistic function has a deeper probabilistic interpretation, which we describe next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log Odds\n",
    "            \n",
    "Recall that the odds are the ratio $p/(1-p)$ for a probability $ p $. For example, when we toss a fair coin, the odds of getting heads are 1; for a coin that's twice as likely to land heads as tails ($p=2/3$), the odds of getting heads are 2. The logistic model is also called the *log odds* model because the logistic function coincides with a linear function of the log odds."
   ]
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   "cell_type": "markdown",
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   "source": [
    "We can see this in the following equations. To show this, we multiply the numerator and denominator of the sigmoid function by $\\exp(t)$: \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sigma(t) & = \\frac{1}{1+\\exp(-t)} = \\frac{\\exp(t)}{1+\\exp(t)} \\\\ \n",
    "\\\\\n",
    "(1-\\sigma(t)) & = 1 - \\frac{\\exp(t)}{1+\\exp(t)} = \\frac{1}{1+\\exp(t)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Then we take the logarithm of the odds and simplify:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\log \\left( \\frac{\\sigma(t)}{1-\\sigma(t)} \\right) & = \\log(\\exp{(t)}) = t\\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, for $\\sigma(\\theta_0 + \\theta_1x)$, we find the log odds are a linear function of $x$:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\log \\left( \\frac{\\sigma(\\theta_0 + \\theta_1x)}{1-\\sigma(\\theta_0 + \\theta_1x)} \\right) & = \\log(\\exp{(\\theta_0 + \\theta_1x)}) = \\theta_0 + \\theta_1x\\\\\n",
    "\\end{aligned}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This representation of the logistic in terms of log odds gives a useful interpretation for the coefficient $\\theta_1$. Suppose the explanatory variable increases by 1. Then the odds change as follows:\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\text{ odds } =& ~ \\exp\\left( \\theta_0 + \\theta_1(x+1) \\right)\\\\\n",
    " =& ~ \\exp(\\theta_1) \\times \\exp{(\\theta_0 + \\theta_1x)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "We see that the odds increase or decrease by a factor of $ \\exp(\\theta_1) $."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "Here, the $\\log$ function is the natural logarithm. Since the natural log is the\n",
    "default in data science, we typically don't bother to write it as $\\ln$.\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, let's add a logistic curve to our plot of proportions to get a sense of how well it might fit the data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using a Logistic Curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the following plot, we've added a logistic curve on top of the plot of proportions of fallen trees:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "trees = trees.assign(log_diam=np.log(trees['diameter']))\n",
    "X = trees[['log_diam']]\n",
    "y = trees['status_0_1']\n",
    "\n",
    "lr_model = LogisticRegression().fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
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   "metadata": {
    "ExecuteTime": {
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    "tags": [
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   },
   "outputs": [
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     },
     "metadata": {},
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    }
   ],
   "source": [
    "X_plt = pd.DataFrame(\n",
    "    {\"log_diam\": np.linspace(X[\"log_diam\"].min(), X[\"log_diam\"].max(), 50)}\n",
    ")\n",
    "p_hats = lr_model.predict_proba(X_plt)\n",
    "X_orig = np.exp(X_plt)\n",
    "\n",
    "fig = px.scatter(\n",
    "    tree_bins, x=\"diameter\", y=\"proportion\", size=\"count\", log_x=True,\n",
    "    labels={\"diameter\": \"Tree diameter (cm)\", \"proportion\": \"Proportion down\"},\n",
    "    width=450, height=250,\n",
    ")\n",
    "\n",
    "fig.add_trace(go.Scatter(\n",
    "    x=X_orig[\"log_diam\"], y=p_hats[:, 1], line=dict(color=\"orange\", width=3),\n",
    "))\n",
    "\n",
    "fig.update_layout(showlegend=False)\n",
    "fig"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "We can see that the curve follows the proportions reasonably well. In fact, we selected this particular logistic by fitting it to the data. The fitted logistic regression is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "σ(-7.4 + 3.0x)\n"
     ]
    }
   ],
   "source": [
    "[t0] = lr_model.intercept_\n",
    "[[t1]] = lr_model.coef_\n",
    "print(f'σ({t0:.1f} + {t1:.1f}x)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we've seen that logistic curves can model probabilities well, we turn\n",
    "to the process of fitting logistic curves to data. In the next section, we\n",
    "proceed to our second step in modeling: selecting an appropriate loss function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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